Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg


Oberseminar Differentialgeometrie


Professor Dr. Christian Bär
Universität Potsdam

spricht am
Montag, 8. Juni 2020
16:00 Uhr
über das Thema:

»Manifolds with many Rarita-Schwinger fields«

The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kähler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension. This is joint work with Rafe Mazzeo.


Hierzu ergeht herzliche Einladung.
Prof. Dr. Bernhard Hanke

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